If global politics strike you as unstable right now, you should see First Snow/Première neige. It’s as if the uncertainty of our times has worked its way into the very form of the play, making it fragile, provisional and volatile. If there’s the opposite of a well-made play, this is it.

A transatlantic co-production by the National Theatre of Scotland and two Quebec companies, Théâtre Pap and Productions Hotel-Motel, it’s ostensibly about the Yes voters in Scotland’s 2014 independence referendum and Quebec’s second referendum of 1995 as they come to terms with being on the losing side. The “what happens next?” question arising from their defeat spills into the narrative and structural shakiness of the play itself. It’s as if they have to will it to continue.

Written by Davey Anderson, Philippe Ducros and Linda McLean, it is set in a family home in Canada, although the family is not a “real” family and the set, by Karen Tennent, is an informal array of mismatched chairs, closer to a rehearsal room than a literal representation. Not only does it glide back and forth between French and English, all translated into two kinds of sign language, but it continually interrupts itself. The actors step out of character, line up to address us directly and stop to argue whether an opinion is their own or part of the story.

Such deconstruction won’t be to everyone’s taste, but Patrice Dubois’s production plays fascinating games as it questions our need for identity and belonging, whether it be in a home, a landscape, a nation or a language. The perspectives in this extended family gathering are many, with cultural backgrounds ranging from English-Canadian to Mexican, and even when they appear to share the same values of liberal self-determination, their cultural heritage points them in very different directions. Thierry Mabonga prefers to speak English in his Scottish accent than switch to the French that for him is not the language of liberation that his Quebecois hosts hear, but the language of his colonial oppressors in the Republic of Congo.

Throw in the varying political experiences of different generations – one person’s 1980 referendum is another’s Arab spring – and the understanding of identity only becomes more diffuse. For Isabelle Vincent as the resident artist trying to resist the role of matriarch, the only logical thing to do is destroy her much-loved painting of the local landscape and start again with a new view. It’s an open-ended conclusion for ambiguous times, but it makes up in needling questions what it lacks in narrative resolve.

Have you ever met Danny Guthrie? More than likely there was a boy just like him at your school. We never meet him for real in Square Go, an intoxicating two-hander by Kieran Hurley and Gary McNair about playground violence and the roots of male dysfunction, but he looms large as an awe-inducing threat, ever ready to wreak violence. In Finn den Hertog’s excellent in-the-round production, Scott Fletcher plays Max, a high-school pupil who has inadvertently provoked the class bully and is now compelled to go through the man-to-man combat of the “square go”.

Abetted but not always aided by Gavin Wright as his best pal Stevie – the two of them in ludicrous school sports gear – he prepares for the inevitable roughing up by invoking macho fantasies of prize fighters and heavy drinkers. Little use observing that playground thugs rarely go on to succeed in life when their agenda of violence carries so much sway right now. Whipping the audience into a frenzy of bullying and chants, Square Go is as funny as it is bleakly true.

Things, of course, are different for girls, although rarely as different as they were for Cora Bissett. Still a teenager with a university place beckoning, she ended up as the lead singer of indie band Darlingheart and suddenly found herself pronounced as the next big thing. In the fascinating, funny and poignant What Girls Are Made Of, she takes centre stage to recount her exploits partying with Blur, keeping her distance from Radiohead and being spat out by a record industry that failed to find a use for her.

Staged as a piece of narrative gig theatre, accompanied by Simon Donaldson (guitar), Susan Bear (drums and keyboards) and Grant O’Rourke (bass), Orla O’Loughlin’s production blends in the sounds of Nirvana, Patti Smith and the Darlingheart hits that never were as it tells a rise-and-fall story of false hopes and bad management. Bissett clearly relishes being back on stage after several years in the director’s seat and if she doesn’t quite make the connection between this story and other life events, including the death of her father and the birth of her daughter, her adult perspective gives emotional depth to an extraordinary tale.

Also mining the territory the French call auto-fiction, actor-turned-playwright Martin McCormick tells his own salutary tale in South Bend. Staged by Grid Iron in an elegant production by Ben Harrison, complete with video backdrop by Lewis den Hertog and live foley sound effects by David A Pollock, it is the true-life story of a childhood obsession with all things American that turned into a love affair with an actual American woman.

“Trust me!” begins McCormick as he invites us to do exactly the opposite in this era of fake news, but it’s his own trusting nature in a woman who seemed to change personality in a matter of months that eventually does for him. Having flown back to Scotland at the end of his studies at the California Institute of the Arts, he gets the call to join her again only to find her – and her mother – unaccountably unwelcoming.

He gives it all he’s got (which is sometimes a little too much) and Jess Chanliau is entertaining as all the supporting characters, but peculiar though some details are, he fails to make the story seem much more extraordinary than the awkward end to any love affair.

• First Snow/Première neige, Canada Hub @ King’s Hall, until 26 August; Square Go, Roundabout @ Summerhall, until 26 August; What Girls Are Made Of, Traverse, until 26 August; South Bend, Gilded Balloon at the Museum, until 27 August

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